Linear estimation pdf

1. What is linear estimate?
2. How do you find the linear estimator?
3. What is estimation space in linear model?
4. How do you find the blue of a linear model?

What is linear estimate?

From Encyclopedia of Mathematics. A linear function of observable random variables, used (when the actual values of the observed variables are substituted into it) as an approximate value (estimate) of an unknown parameter of the stochastic model under analysis (see Statistical estimator).

How do you find the linear estimator?

The linear MMSE estimator of the random variable X, given that we have observed Y, is given by ˆXL=Cov(X,Y)Var(Y)(Y−EY)+EX=ρσXσY(Y−EY)+EX. The estimation error, defined as ˜X=X−ˆXL, satisfies the orthogonality principle: E[˜X]=0,Cov(˜X,Y)=E[˜XY]=0.

What is estimation space in linear model?

Estimation space is defined as the column space of X and error space is defined as the orthogonal complement of the estimation space, i.e. the null space of XT.

How do you find the blue of a linear model?

Find the linear estimator that is unbiased and has minimum variance. This leads to Best Linear Unbiased Estimator (BLUE) To find a BLUE estimator, full knowledge of PDF is not needed. Just the first two moments (mean and variance) of the PDF is sufficient for finding the BLUE.